In one type of frequency output sensor, a force is converted to a frequency by a vibrating beam force sensing element. The force sensing element is coupled to a drive circuit that causes the force sensing element to vibrate at its resonant frequency. A tension force on the force sensing element causes its resonant frequency to rise, while a compression force on the force sensing element causes its resonant frequency to decrease. The force sensing element can therefore be operated as a force-to-frequency converter that frequency modulates an information signal onto a carrier signal, the carrier signal being the zero load resonant frequency of the force sensing element. A significant advantage of frequency output sensors is the fact that their output signals are inherently digital, and may therefore be conveniently integrated into a microprocessor-based system.
The output signal of a frequency output sensor may be demodulated by counting the number of cycles of the output signal that occur in each of a series of sampling intervals. For each sampling interval, the average frequency during that sampling interval is determined by dividing the number of cycles by the length of the sampling interval. Systems of this type sample a continuously variable quantity (frequency) at a sequence of sampling times. Such systems are therefore susceptible to aliasing of high frequency inputs, e.g., high frequency forces such as vibrations, when the frequency of such inputs exceeds the Nyquist frequency that is equal to half of the sampling frequency.
The aliasing problem can be better appreciated by considering the specific example of a vibrating beam accelerometer. In such an instrument, acceleration along the instrument's sensitive axis causes a compression or tension force on a vibrating beam force sensing element. Such an instrument may have a mechanical resonance in the range 1200-3000 Hz, and may have its output signal sampled at a rate on the order of 400 Hz. As a result, if the structure to which the accelerometer is attached vibrates at or near the frequency of the mechanical resonance, the vibration will be aliased into the sensor's bandwidth.
Such aliasing may not significantly degrade the performance of the accelerometer for certain applications, such as navigation systems. This is due to the fact that it is an inherent property of such a sensor that no vibrations will alias to DC (i.e., zero Hz), because the sensor has no frequency response at multiples of the sampling frequency. Furthermore, aliased components at frequencies other than DC may have little effect, because such signals average out when the acceleration is integrated to determine velocity and position. However, when a frequency output accelerometer is used in an autopilot, for example, such aliasing has the potential for causing spurious steering commands at low frequencies (within the instrument's bandwidth), thereby reducing aerodynamic efficiency and increasing autopilot power consumption.
The normal digital system practice to minimize the effects of aliasing is to use analog filters before sampling, to attenuate high frequencies to an acceptable level. However, in a frequency output accelerometer, there is direct mechanical conversion of the input acceleration into a frequency output. Therefore, to prevent or minimize aliasing, one is limited either to mechanical filtering, so that high frequency vibrations do not reach the accelerometer, or to the use of digital filtering after the sampling process. Mechanical filtering, such as with mechanical isolators, has the disadvantage that the isolator increases the size of the components making up the system. In addition, mechanical isolators have poor dimensional stability, and are subject to aging effects. The use of digital filtering after sampling generally requires a very high sampling rate, and therefore imposes large throughput requirements on the digital processing system.
In an FM communications system, filtering to reduce bandwidth can be performed on the information signal either prior to modulation in the transmitter, or after demodulation in the receiver. Such filtering is performed in a conventional way in the amplitude domain, i.e., the signal being filtered is one in which the information is encoded as the amplitude of a waveform with respect to a zero or reference level. Such filtering is distinct from the filtering of a frequency domain signal, i.e., a signal in which the information is encoded as the frequency of the signal with respect to a referenced frequency. It is known from FM communications systems theory that the frequency spectrum of an FM signal comprises a central peak, corresponding to the carrier frequency, and side bands that represent the information carried by the signal. In such communications systems, a possible technique for limiting the bandwidth of the system is to pass the FM signal through a band-pass filter that symmetrically attenuates frequencies beyond a certain distance from the carrier. However, it is also known that such a process produces a nonlinear effect on the frequency components carried by the signal. While such nonlinearities could be unimportant in some FM systems, they would significantly degrade the accuracy of a frequency output sensor. There is therefore a need for an anti-aliasing technique for frequency output sensors that does not introduce nonlinearities, and that does not require mechanical isolators or very high sampling rates.